Evaluate. (-7)^((5)/(3))*((1)/(56))^((5)/(3))=

Identify Equation: Identify the equation and apply the property of exponents for multiplication. We have two terms with the same exponent, so we can combine them under the same exponent: (-7)^(5/3) * (1/56)^(5/3) = [(-7) * (1/56)]^(5/3)Simplify Multiplication: Simplify the multiplication inside the brackets. (-7) * (1/56) = -1/8Write Single Power: Write the simplified multiplication as a single power. [(-7) * (1/56)]^(5/3) = (-1/8)^(5/3)Break Down Exponent: Break down the exponent (5/3) into a whole number part and a fractional part. The exponent 5/3 can be thought of as an exponent of 1 (the cube root) followed by an exponent of 5 (raising to the fifth power): (-1/8)^(5/3) = [(-1/8)^(1/3)]^5Calculate Cube Root: Calculate the cube root of -1/8. The cube root of -1 is -1, and the cube root of 1/8 is 1/2, so: (-1/8)^(1/3) = -1/2Raise to Fifth Power: Raise the result of the cube root to the fifth power. (-1/2)^5 = -1/32

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Evaluate.

(-7)^((5)/(3))*((1)/(56))^((5)/(3))=

Evaluate. $\newline$ $(-7)^{\frac{5}{3}} \cdot\left(\frac{1}{56}\right)^{\frac{5}{3}}=$

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Math Problems

Algebra 1

Simplify radical expressions involving fractions

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Q. Evaluate.

\newline

(-7)^{\frac{5}{3}} \cdot\left(\frac{1}{56}\right)^{\frac{5}{3}}=

Identify Equation: Identify the equation and apply the property of exponents for multiplication. $\newline$ We have two terms with the same exponent, so we can combine them under the same exponent: $\newline$ (\(-7)^{\frac{ $5$ }{ $3$ }} \times \left(\frac{ $1$ }{ $56$ }\right)^{\frac{ $5$ }{ $3$ }} = \left[( $-7$ ) \times \left(\frac{ $1$ }{ $56$ }\right)\right]^{\frac{ $5$ }{ $3$ }}
Simplify Multiplication: Simplify the multiplication inside the brackets. $\newline$ $(-7) \times (1/56) = -1/8$
Write Single Power: Write the simplified multiplication as a single power. $\newline$ $[(-7) \times (1/56)]^{5/3} = (-1/8)^{5/3}$
Break Down Exponent: Break down the exponent $(5/3)$ into a whole number part and a fractional part. $\newline$ The exponent $5/3$ can be thought of as an exponent of $1$ (the cube root) followed by an exponent of $5$ (raising to the fifth power): $\newline$ $(-1/8)^{(5/3)} = [(-1/8)^{(1/3)}]^5$
Calculate Cube Root: Calculate the cube root of $-\frac{1}{8}$ . The cube root of $-1$ is $-1$ , and the cube root of $\frac{1}{8}$ is $\frac{1}{2}$ , so: $(-\frac{1}{8})^{\frac{1}{3}} = -\frac{1}{2}$
Raise to Fifth Power: Raise the result of the cube root to the fifth power. $(-\frac{1}{2})^5 = -\frac{1}{32}$