The expression root(4)(5^(3))*root(4)(5^(5)) is equivalent to 5^(2) 5^((15)/(16)) 25^((15)/(16)) 25^(2)

Understand the problem: Understand the problem. We need to simplify the expression which involves fourth roots of powers of 5.Apply exponent property: Apply the property of exponents for roots. The fourth root of a number is the same as raising that number to the 1/4 power. root(4)(5^(3)) * root(4)(5^(5)) = 5^(3/4) * 5^(5/4)Add exponents: Add the exponents since the bases are the same. When multiplying with the same base, add the exponents. 5^(3/4) * 5^(5/4) = 5^((3/4) + (5/4))Perform addition: Perform the addition of the exponents. (3/4) + (5/4) = (3+5)/4 = 8/4Simplify exponent: Simplify the exponent. 8/4 simplifies to 2. 5^((3/4) + (5/4)) = 5^(8/4) = 5^2Write final answer: Write the final answer. The simplified form of the expression is 5^2.

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The expression
root(4)(5^(3))*root(4)(5^(5)) is equivalent to

5^(2)

5^((15)/(16))

25^((15)/(16))

25^(2)

The expression $\sqrt[4]{5^{3}} \cdot \sqrt[4]{5^{5}}$ is equivalent to $\newline$ $5^{2}$ $\newline$ $5^{\frac{15}{16}}$ $\newline$ $25^{\frac{15}{16}}$ $\newline$ $25^{2}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\sqrt[4]{5^{3}} \cdot \sqrt[4]{5^{5}}

is equivalent to

\newline

5^{2}

\newline

5^{\frac{15}{16}}

\newline

25^{\frac{15}{16}}

\newline

25^{2}

Understand the problem: Understand the problem. We need to simplify the expression which involves fourth roots of powers of $5$ .
Apply exponent property: Apply the property of exponents for roots. $\newline$ The fourth root of a number is the same as raising that number to the $\frac{1}{4}$ power. $\newline$ $\sqrt[4]{5^{3}} \times \sqrt[4]{5^{5}} = 5^{\frac{3}{4}} \times 5^{\frac{5}{4}}$
Add exponents: Add the exponents since the bases are the same. $\newline$ When multiplying with the same base, add the exponents. $\newline$ $5^{\frac{3}{4}} \times 5^{\frac{5}{4}} = 5^{\left(\frac{3}{4} + \frac{5}{4}\right)}$
Perform addition: Perform the addition of the exponents. $\newline$ $(\frac{3}{4}) + (\frac{5}{4}) = (\frac{3+5}{4}) = \frac{8}{4}$
Simplify exponent: Simplify the exponent. $\newline$ $\frac{8}{4}$ simplifies to $2$ . $\newline$ $5^{(\frac{3}{4} + \frac{5}{4})} = 5^{\frac{8}{4}} = 5^2$
Write final answer: Write the final answer. $\newline$ The simplified form of the expression is $5^2$ .