Question

Simplify using Exponent Rules: 74×7×713×7−20 (1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

We can simplify using the exponent rules:

74 × 7 × 713 × 7^(-20)

First, let's simplify the multiplication: 74 × 7 = 518.

Now, let's simplify the exponent rule: 7^(-20) = 1 / 7^20.

Therefore, the simplified expression is 518 × 713 × (1 / 7^20).

Answer 2

Simplify using Exponent Rules: 74×7×713×7−20 (1 point)

28^-2

1/7^2

1/7^3

1/7^-2

Answer 3

[AI-generated answer — Bot GPT 3.5]

To simplify 28^(-2), which means "28 raised to the power of -2," we can apply the exponent rule that states a negative exponent is equal to 1 divided by the number raised to the positive exponent:

28^(-2) = 1 / 28^2

Similarly, for 7^(-2) and 7^(-3), we have:

7^(-2) = 1 / 7^2

and

7^(-3) = 1 / 7^3

However, the last expression, 1/7^(-2), needs to be rewritten using exponent rules. A negative exponent in the denominator indicates that the base should move to the numerator.

1/7^(-2) = 7^2

So the simplified expressions are:

28^(-2) = 1 / 28^2

7^(-2) = 1 / 7^2

7^(-3) = 1 / 7^3

1/7^(-2) = 7^2

Answer 4

Simplify using Exponent Rules: 7^4×7×7^13×7^−20 (1 point)

28^-2

1/7^2

1/7^3

1/7^-2

Answer 5

[AI-generated answer — Bot GPT 3.5]

To simplify 7^4 × 7 × 7^13 × 7^(-20), we can apply the exponent rule that states when multiplying with the same base, we add the exponents:

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

Now, we can simplify the exponent:

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

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

Therefore, the correct answer is "28^-2".

Answer 6

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

1^4

5^2

25^4

5^4

Answer 7

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (5^8/5^6)^2 using the exponent rules, we can apply the rule that when dividing with the same base, we subtract the exponents:

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

Simplifying the exponent:

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

Simplifying further:

5^2^2 = 5^4

So, the fully simplified expression is 5^4.

Therefore, the correct answer is 5^4.

Answer 8

Simplify using the Exponent Rules: (Your answer can have only positive exponents) (x^3) (x^-6)/(x^2)^5

x^7

1/x^28

1/x^13

x^8

Answer 9

[AI-generated answer — Bot GPT 3.5]

To simplify the expression (x^3) (x^-6)/(x^2)^5 using the exponent rules, we can apply the rules for multiplying and dividing exponents with the same base:

(x^3) (x^-6)/(x^2)^5 = x^(3 + (-6) - 5 * 2)

Simplifying the exponents:

x^(3 + (-6) - 5 * 2) = x^(3 - 6 - 10)

Further simplifying:

x^(3 - 6 - 10) = x^(-13)

Since we need the answer to have only positive exponents, we can rewrite x^(-13) as 1/x^13.

So, the simplified expression is 1/x^13.

Therefore, the correct answer is 1/x^13.

Answer 10

[AI-generated answer — Explain Bot]

To simplify the given expression using exponent rules, we need to understand the rules for multiplying and dividing numbers with exponents.

First, let's rewrite the expression with the exponents clearly indicated:
\(7^4 \times 7^3 \times 7^3 \times 7^{-20}\)

Using the multiplication rule of exponents, when multiplying numbers with the same base, we add the exponents. So, applying this rule, we get:
\(7^{4+3+3} \times 7^{-20}\)

Simplifying further gives:
\(7^{10} \times 7^{-20}\)

Using the division rule of exponents, which states that when dividing numbers with the same base, we subtract the exponents, we can rewrite the expression as:
\(7^{10-20}\)

Finally, subtracting the exponents gives us:
\(7^{-10}\)

Therefore, the simplified form of the expression \(74 \times 7 \times 713 \times 7^{-20}\) is \(7^{-10}\).