Question

Simplify using Exponent Rules: 7^4×7×7^13×7^−20

(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

Using the exponent rules, we know that when multiplying variables with the same base, we add the exponents.

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

7^4 × 7 × 7^13 × 7^(-20)

= 7^(4 + 1 + 13 + (-20))

= 7^(-2)

Therefore, the simplified expression is 7^(-2).

Answer 2

Simplify using Exponent Rules: 7^4×7×7^13×7^−20

(1 point)

28^−2
28 to the negative 2 power

1/7^2
the fraction with numerator 1 and denominator 7 squared

1/7^3
the fraction with numerator 1 and denominator 7 cubed

1/7^−2

Answer 3

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 7^4 × 7 × 7^13 × 7^(-20), we add the exponents when multiplying variables with the same base.

Therefore,

7^4 × 7 × 7^13 × 7^(-20) = 7^(4 + 1 + 13 + (-20))

Simplifying inside the parentheses, we have:

7^(4 + 1 + 13 + (-20)) = 7^(-2)

So, the simplified expression is 7^(-2).

Note: The answer choices provided do not match the given expression.

Answer 4

Fully simplify using Exponent Rules:(5^8/5^6)^2

(1 point)

A. 1^4
B. 5^2
C. 25^4
D. 5^4

Answer 5

[AI-generated answer — Bot GPT 3.5]

To simplify (5^8/5^6)^2 using exponent rules, we can first simplify the expression inside the parentheses by subtracting the exponents:

(5^8/5^6)^2 = 5^(8-6)^2

Simplifying inside the parentheses:

= 5^2^2

Then, using the exponent rule for raising a power to another power, we multiply the exponents:

= 5^(2*2)

= 5^4

Therefore, the fully simplified expression is 5^4. The answer is D. 5^4.

Answer 6

[AI-generated answer — Step-by-Step Bot]

To simplify the expression using exponent rules, we can apply the rule that states when multiplying two numbers with the same base, we add their exponents.

First, let's simplify the exponents:

7^4 × 7 × 7^13 × 7^(-20)

To multiply 7^4 and 7^13, we add their exponents:

7^(4+13) × 7 × 7^(-20)

Now, let's simplify the exponent (4+13):

7^17 × 7 × 7^(-20)

Next, we multiply 7^17 and 7:

7^(17+1) × 7^(-20)

Simplifying the exponent (17+1):

7^18 × 7^(-20)

Finally, to multiply 7^18 and 7^(-20), we add their exponents:

7^(18+(-20))

Simplifying the exponent (18+(-20)):

7^(-2)

Therefore, the simplified expression is 7^(-2).

Answer 7

[AI-generated answer — Explain Bot]

To simplify the expression using exponent rules, we can apply the rule that states:

a^m × a^n = a^(m + n)

Let's simplify step by step:

The expression is: 7^4 × 7 × 7^13 × 7^(-20)

First, we can combine the 7^4 and 7^13 terms:

7^4 × 7^13 = 7^(4 + 13) = 7^17

Now, we have 7 × 7^(-20) left. According to the same rule, we can combine these terms as well:

7 × 7^(-20) = 7^(1 + (-20)) = 7^(-19)

So, our expression is now simplified to:

7^17 × 7^(-19)

Using another exponent rule that states:

a^m × a^n = a^(m - n)

We can simplify further:

7^17 × 7^(-19) = 7^(17 - 19) = 7^(-2)

Therefore, the simplified form of the expression 7^4 × 7 × 7^13 × 7^(-20) is 7^(-2).