Simplify. ((x^(4))/(7^(-8)))^(-7)

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Bytelearn · Accepted Answer

Understand Problem: Understand the problem and rewrite the expression using the properties of exponents. The problem asks us to simplify the expression ((x^(4))/(7^(-8)))^(-7). We can start by simplifying the expression inside the parentheses using the property of exponents that states a^(-n) = 1/(a^n).Apply Exponent Property: Apply the exponent property to the denominator. Since 7^(-8) is in the denominator, we can rewrite it as 7^(8) in the numerator. ((x^(4))*(7^(8)))^(-7)Apply Power Rule: Apply the power of a power rule. The power of a power rule states that (a^(m))^n = a^(m*n). We will apply this rule to both x^(4) and 7^(8). (x^(4*(-7)))*(7^(8*(-7)))Multiply Exponents: Multiply the exponents. Now we multiply the exponents inside the parentheses by -7. x^(-28)*7^(-56)Rewrite Negative Exponents: Rewrite negative exponents as fractions. Negative exponents indicate the reciprocal of the base raised to the positive exponent. So we rewrite x^(-28) and 7^(-56) as fractions. 1/(x^(28)) * 1/(7^(56))Combine Fractions: Combine the fractions. Since both terms are in the denominator, we can combine them into a single fraction. 1/((x^(28))*(7^(56)))

Simplify. $\left(\frac{x^{4}}{7^{-8}}\right)^{-7}$

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