Select the equivalent expression. ((3^(-6))/(7^(-3)))^(5)=? Choose 1 answer: (A) (7^(3))/(3^(-30)) (B) (7^(15))/(3^(30)) (c) (3^(15))/(7^(30))

Simplify expression using exponent property: Simplify the expression inside the parentheses by using the property of exponents that states a^(-n) = 1/(a^n). ((3^(-6))/(7^(-3))) can be rewritten as (1/(3^6))/(1/(7^3)).Multiply by reciprocal of divisor: When dividing fractions, you multiply by the reciprocal of the divisor. So, (1/(3^6))/(1/(7^3)) becomes (1/(3^6)) * (7^3).Simplify resulting expression: Simplify the expression obtained in Step 2. This results in (7^3)/(3^6).Raise fraction to power of 5: Now raise the simplified fraction to the power of 5, which is the same as raising both the numerator and the denominator to the power of 5. So, ((7^3)/(3^6))^5 becomes (7^(3*5))/(3^(6*5)).Calculate exponents: Calculate the exponents. 3*5 equals 15, and 6*5 equals 30. So, the expression becomes (7^15)/(3^30).Match result with choices: Match the result with the given choices. The expression (7^15)/(3^30) corresponds to choice (B).

Home

Math Problems

Grade 8

Evaluate expressions using properties of exponents

Full solution

Q. Select the equivalent expression.

\newline

\left(\frac{3^{-6}}{7^{-3}}\right)^{5}=?

\newline

Choose

1

answer:

\newline

(A)

\frac{7^{3}}{3^{-30}}

\newline

(B)

\frac{7^{15}}{3^{30}}

\newline

(C)

\frac{3^{15}}{7^{30}}

Simplify expression using exponent property: Simplify the expression inside the parentheses by using the property of exponents that states $a^{-n} = \frac{1}{a^n}$ . $\newline$ $\left(\frac{3^{-6}}{7^{-3}}\right)$ can be rewritten as $\left(\frac{1}{3^6}\right)/\left(\frac{1}{7^3}\right)$ .
Multiply by reciprocal of divisor: When dividing fractions, you multiply by the reciprocal of the divisor. So, $(1/(3^6))/(1/(7^3))$ becomes $(1/(3^6)) \times (7^3)$ .
Simplify resulting expression: Simplify the expression obtained in Step $2$ . This results in $(7^3)/(3^6)$ .
Raise fraction to power of $5$ : Now raise the simplified fraction to the power of $5$ , which is the same as raising both the numerator and the denominator to the power of $5$ . So, $\left(\frac{7^3}{3^6}\right)^5$ becomes $\frac{7^{3 \cdot 5}}{3^{6 \cdot 5}}$ .
Calculate exponents: Calculate the exponents. $3 \times 5$ equals $15$ , and $6 \times 5$ equals $30$ . So, the expression becomes $(7^{15})/(3^{30})$ .
Match result with choices: Match the result with the given choices. The expression $(7^{15})/(3^{30})$ corresponds to choice (B).