Evaluate. 243^((7)/(10))*243^((1)/(10))=

Recognize properties of exponents: Recognize the properties of exponents. When multiplying two expressions with the same base, you can add the exponents. 243^(7/10) * 243^(1/10) = 243^(7/10 + 1/10)Add exponents: Add the exponents. 7/10 + 1/10 = 8/10 Simplify the fraction 8/10 to its lowest terms. 8/10 = 4/5 So, 243^(7/10) * 243^(1/10) = 243^(4/5)Simplify fraction: Evaluate the expression. 243 is 3 raised to the 5th power (3^5), which can be useful when dealing with fractional exponents. 243^(4/5) = (3^5)^(4/5) Use the property of exponents (a^(m))^n = a^(m*n). (3^5)^(4/5) = 3^(5*4/5)Evaluate expression: Simplify the exponent. 5*4/5 = 4 So, 3^(5*4/5) = 3^4Simplify exponent: Calculate the value of 3^4. 3^4 = 3 * 3 * 3 * 3 3^4 = 81

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Evaluate.

243^((7)/(10))*243^((1)/(10))=

Evaluate. $\newline$ $243^{\frac{7}{10}} \cdot 243^{\frac{1}{10}}=$

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Math Problems

Algebra 1

Solve multi-step linear equations

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Q. Evaluate.

\newline

243^{\frac{7}{10}} \cdot 243^{\frac{1}{10}}=

Recognize properties of exponents: Recognize the properties of exponents. $\newline$ When multiplying two expressions with the same base, you can add the exponents. $\newline$ $243^{7/10} \times 243^{1/10} = 243^{7/10 + 1/10}$
Add exponents: Add the exponents. $\newline$ $\frac{7}{10} + \frac{1}{10} = \frac{8}{10}$ $\newline$ Simplify the fraction $\frac{8}{10}$ to its lowest terms. $\newline$ $\frac{8}{10} = \frac{4}{5}$ $\newline$ So, $243^{\frac{7}{10}} \times 243^{\frac{1}{10}} = 243^{\frac{4}{5}}$
Simplify fraction: Evaluate the expression. $\newline$ $243$ is $3$ raised to the $5$ th power $(3^5)$ , which can be useful when dealing with fractional exponents. $\newline$ $243^{\frac{4}{5}} = (3^5)^{\frac{4}{5}}$ $\newline$ Use the property of exponents $(a^{m})^{n} = a^{m*n}$ . $\newline$ $(3^5)^{\frac{4}{5}} = 3^{5*\frac{4}{5}}$
Evaluate expression: Simplify the exponent. $\newline$ $5\times\frac{4}{5} = 4$ $\newline$ So, $3^{5\times\frac{4}{5}} = 3^4$
Simplify exponent: Calculate the value of $3^4$ . $\newline$ $3^4 = 3 \times 3 \times 3 \times 3$ $\newline$ $3^4 = 81$