Question

which expression is correctly developed to use the product rules of exponents

Answer 1

[AI-generated answer — Bot GPT 3.5]

The correct expression developed using the product rule of exponents is:

\(x^{a} \cdot x^{b} = x^{a+b}\)

Answer 2

find the numerical equivalent of 10^(2) 10^(3)

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the numerical equivalent of \(10^2 \cdot 10^3\), we can apply the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\).

Using this rule, we can simplify the expression as follows:

\(10^2 \cdot 10^3 = 10^{2+3} = 10^5\)

Therefore, \(10^2 \cdot 10^3\) is equal to \(10^5\), which is equal to 100,000.

Answer 4

which of the following correctly use the product rule of exponents to simplify the expression 100^(8) 100^(7)

Answer 5

[AI-generated answer — Bot GPT 3.5]

To simplify the expression \(100^8 \cdot 100^7\), we can use the product rule of exponents: \(a^m \cdot a^n = a^{m+n}\).

Using this rule, we can simplify the expression as follows:

\(100^8 \cdot 100^7 = 100^{8+7} = 100^{15}\)

Therefore, the correct expression using the product rule of exponents to simplify the expression is \(100^{8+7}\).

Answer 6

Find the numerical equivalent of 2^(5) 2^(-2)

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the numerical equivalent of \(2^5 \cdot 2^{-2}\), we can apply the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\).

Using this rule, we can simplify the expression as follows:

\(2^5 \cdot 2^{-2} = 2^{5 + (-2)} = 2^3\)

Therefore, \(2^5 \cdot 2^{-2}\) is equal to \(2^3\), which equals 8.

Answer 8

Find the numerical equivalent 10^(9) 10^(-7)

Answer 9

[AI-generated answer — Bot GPT 3.5]

To find the numerical equivalent of \(10^9 \cdot 10^{-7}\), we can apply the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\).

Using this rule, we can simplify the expression as follows:

\(10^9 \cdot 10^{-7} = 10^{9 + (-7)} = 10^2\)

Therefore, \(10^9 \cdot 10^{-7}\) is equal to \(10^2\), which equals 100.

Answer 10

Find the numerical equivalent of 4^(9) 4^(-7)

Answer 11

[AI-generated answer — Bot GPT 3.5]

To find the numerical equivalent of \(4^9 \cdot 4^{-7}\), we can apply the product rule of exponents, which states that \(a^m \cdot a^n = a^{m+n}\).

Using this rule, we can simplify the expression as follows:

\(4^9 \cdot 4^{-7} = 4^{9 + (-7)} = 4^2\)

Therefore, \(4^9 \cdot 4^{-7}\) is equal to \(4^2\), which equals 16.

Answer 12

which expression is correctly developed to use the product rule of exponents

10^(8) 10^(8)

32^(7)

6^(2) 7^(3)

5^((2))^9

Answer 13

[AI-generated answer — Bot GPT 3.5]

The expression that is correctly developed to use the product rule of exponents is:

10^(8) 10^(8)

Using the product rule of exponents, we can simplify this expression as:

10^(8+8) = 10^(16)

Answer 14

Simplify the expression using the quotient rule of integer exponents: t400/t400

t^(4)

300

t^(500)

t^(300)

Answer 15

[AI-generated answer — Bot GPT 3.5]

To simplify the expression \(\frac{t^{400}}{t^{400}}\) using the quotient rule of exponents, we subtract the exponents:

\[t^{400-400} = t^0\]

Any non-zero number raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:

\[t^0 = 1\]

Answer 16

simplify a^(67)/b^(34)

Answer 17

[AI-generated answer — Bot GPT 3.5]

To simplify the expression \(\frac{a^{67}}{b^{34}}\) using the quotient rule of exponents, we subtract the exponents:

\(\frac{a^{67}}{b^{34}} = a^{67 - 34}\)

Simplifying the exponent, we have:

\(a^{67 - 34} = a^{33}\)

Therefore, the simplified expression is \(a^{33}\).

Answer 18

apply the quotient rule of integer exponents to simplify 23^(65) / 23^(32)

Answer 19

[AI-generated answer — Bot GPT 3.5]

To simplify the expression \(\frac{23^{65}}{23^{32}}\) using the quotient rule of integer exponents, we subtract the exponents:

\(\frac{23^{65}}{23^{32}} = 23^{65 - 32}\)

Simplifying the exponent, we have:

\(23^{65 - 32} = 23^{33}\)

Therefore, the simplified expression is \(23^{33}\).

Answer 20

simplify this expression using the quotient rule of integer exponents

12^(53) / 7^(53)

Answer 21

[AI-generated answer — Bot GPT 3.5]

To simplify the expression \(\frac{12^{53}}{7^{53}}\) using the quotient rule of integer exponents, we subtract the exponents:

\(\frac{12^{53}}{7^{53}} = 12^{53 - 53}\)

Simplifying the exponent, we have:

\(12^{53 - 53} = 12^0\)

Any non-zero number raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:

\(12^0 = 1\)

Answer 22

12^(53) / 7^(53)

Answer 23

[AI-generated answer — Bot GPT 3.5]

To simplify the expression \(\frac{12^{53}}{7^{53}}\), we can rewrite it as a single exponent:

\(\frac{12^{53}}{7^{53}} = \left(\frac{12}{7}\right)^{53}\)

Therefore, the simplified expression is \(\left(\frac{12}{7}\right)^{53}\).

Answer 24

12^(53) divided by 7^(53)

Answer 25

[AI-generated answer — Bot GPT 3.5]

To simplify the expression \(\frac{12^{53}}{7^{53}}\), we can use the quotient rule of exponents, which states that \(a^m \div a^n = a^{m-n}\).

Applying this rule, we subtract the exponents:

\(\frac{12^{53}}{7^{53}} = 12^{53-53} \div 7^{53-53} = 12^{0} \div 7^{0}\)

Any number raised to the power of 0 is equal to 1. Therefore, the expression simplifies to:

\(12^{0} \div 7^{0} = 1 \div 1 = 1\)

Answer 26

what are the correct steps to follow to simplify an exponential expression using the quotient rule of integer exponents

Answer 27

[AI-generated answer — Bot GPT 3.5]

To simplify an exponential expression using the quotient rule of integer exponents, follow these steps:

1. Identify the base of each term in the expression.
2. Determine the exponents of each term.
3. Write the expression as a fraction, with the numerator being the term with the numerator exponent and the denominator being the term with the denominator exponent.
4. Subtract the exponents: numerator exponent minus denominator exponent.
5. Simplify the resulting fraction if possible.
6. Rewrite the expression using the simplified exponent.

For example, to simplify \(a^m / a^n\) using the quotient rule, you would:

1. Identify the base as \(a\).
2. Determine the exponents, \(m\) and \(n\).
3. Write the expression as \(a^m / a^n\).
4. Subtract the exponents: \(m - n\).
5. Simplify the resulting fraction if possible.
6. Rewrite the expression as \(a^{(m-n)}\).