Evaluate: 49^((3)/(2))?

Identify Base and Exponent: Identify the base and the exponent in 49^(3/2). In 49^(3/2), Base: 49 Exponent: 3/2Express as Power of 2: Express 49 as a term raised to the power of 2, since 49 is a perfect square. 49 = 7*7 = 7^2Apply Exponent to Base: Apply the exponent to the base expressed as a power. (7^2)^(3/2) Use the power of a power rule, which states that (a^m)^n = a^(m*n). 7^(2*(3/2))Multiply Exponents: Multiply the exponents. 2 * (3/2) = 3Simplify Expression: Simplify the expression. 7^(2*(3/2)) = 7^3Calculate Value: Calculate the value of 7 raised to the power of 3. 7^3 = 7 * 7 * 7 = 49 * 7 = 343

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Evaluate: $49^{\left(\frac{3}{2}\right)}?$

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Algebra 2

Evaluate rational exponents

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Q. Evaluate:

49^{\left(\frac{3}{2}\right)}?

Identify Base and Exponent: Identify the base and the exponent in $49^{\frac{3}{2}}$ . $\newline$ In $49^{\frac{3}{2}}$ , $\newline$ Base: $49$ $\newline$ Exponent: $\frac{3}{2}$
Express as Power of $2$ : Express $49$ as a term raised to the power of $2$ , since $49$ is a perfect square. $\newline$ $49 = 7 \times 7$ $\newline$ $= 7^2$
Apply Exponent to Base: Apply the exponent to the base expressed as a power. $\newline$ $(7^2)^{\frac{3}{2}}$ $\newline$ Use the power of a power rule, which states that $(a^m)^n = a^{m*n}$ . $\newline$ $7^{2*\left(\frac{3}{2}\right)}$
Multiply Exponents: Multiply the exponents. $2 \times \left(\frac{3}{2}\right) = 3$
Simplify Expression: Simplify the expression. $7^{2*(3/2)} = 7^3$
Calculate Value: Calculate the value of $7$ raised to the power of $3$ . $\newline$ $7^3 = 7 \times 7 \times 7$ $\newline$ $= 49 \times 7$ $\newline$ $= 343$