The expression sqrt5*sqrt(5^(3)) is equivalent to 5^((1)/(2)) 5^((3)/(4)) 5^((4)/(3)) 5^(2)

Understand the Problem: Understand the problem. We need to simplify the expression sqrt(5) * sqrt(5^3).Rewrite in Exponent Form: Rewrite the square roots in exponent form. sqrt(5) can be written as 5^(1/2) and sqrt(5^3) can be written as (5^3)^(1/2).Apply Exponent Rule: Apply the exponent rule (a^n)^m = a^(n*m) to the second term. (5^3)^(1/2) = 5^(3*(1/2)) = 5^(3/2).Multiply Expressions: Multiply the two expressions. 5^(1/2) * 5^(3/2).Apply Exponent Rule: Apply the exponent rule a^m * a^n = a^(m+n) when multiplying two exponents with the same base. 5^(1/2 + 3/2) = 5^(4/2).Simplify Exponent: Simplify the exponent. 5^(4/2) = 5^2.

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The expression
sqrt5*sqrt(5^(3)) is equivalent to

5^((1)/(2))

5^((3)/(4))

5^((4)/(3))

5^(2)

The expression $\sqrt{5} \cdot \sqrt{5^{3}}$ is equivalent to $\newline$ $5^{\frac{1}{2}}$ $\newline$ $5^{\frac{3}{4}}$ $\newline$ $5^{\frac{4}{3}}$ $\newline$ $5^{2}$

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. The expression

\sqrt{5} \cdot \sqrt{5^{3}}

is equivalent to

\newline

5^{\frac{1}{2}}

\newline

5^{\frac{3}{4}}

\newline

5^{\frac{4}{3}}

\newline

5^{2}

Understand the Problem: Understand the problem. We need to simplify the expression $\sqrt{5} \times \sqrt{5^3}$ .
Rewrite in Exponent Form: Rewrite the square roots in exponent form. $\sqrt{5}$ can be written as $5^{1/2}$ and $\sqrt{5^3}$ can be written as $(5^3)^{1/2}$ .
Apply Exponent Rule: Apply the exponent rule $(a^n)^m = a^{n*m}$ to the second term. $\newline$ $(5^3)^{1/2} = 5^{3*(1/2)} = 5^{3/2}$ .
Multiply Expressions: Multiply the two expressions. $5^{\frac{1}{2}} \times 5^{\frac{3}{2}}$ .
Apply Exponent Rule: Apply the exponent rule $a^m \times a^n = a^{m+n}$ when multiplying two exponents with the same base. $\newline$ $5^{\frac{1}{2} + \frac{3}{2}} = 5^{\frac{4}{2}}$ .
Simplify Exponent: Simplify the exponent. $5^{\frac{4}{2}} = 5^2$ .