Understand the expression: Understand the expression 243^(1/5). The expression represents the fifth root of 243, which means we are looking for a number that, when raised to the power of 5, gives 243.Recognize 243 as power of 3: Recognize that 243 is a power of 3. 243 is 3 raised to the 5th power, since 3 * 3 * 3 * 3 * 3 = 243.Apply property of exponents: Apply the property of exponents (a^(m/n) = n√(a^m)). Using this property, we can rewrite 243^(1/5) as the fifth root of 243, which is the same as the fifth root of 3^5.Simplify the expression: Simplify the expression. Since the fifth root of 3^5 is 3, the expression 243^(1/5) simplifies to 3.

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$243^{\frac{1}{5}}=$

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Math Problems

Grade 7

Powers with negative bases

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243^{\frac{1}{5}}=

Understand the expression: Understand the expression $243^{(1/5)}$ . $\newline$ The expression represents the fifth root of $243$ , which means we are looking for a number that, when raised to the power of $5$ , gives $243$ .
Recognize $243$ as power of $3$ : Recognize that $243$ is a power of $3$ . $243$ is $3$ raised to the $5$ th power, since $3 \times 3 \times 3 \times 3 \times 3 = 243$ .
Apply property of exponents: Apply the property of exponents $a^{\frac{m}{n}} = \sqrt[n]{a^m}$ . Using this property, we can rewrite $243^{\frac{1}{5}}$ as the fifth root of $243$ , which is the same as the fifth root of $3^5$ .
Simplify the expression: Simplify the expression. $\newline$ Since the fifth root of $3^5$ is $3$ , the expression $243^{1/5}$ simplifies to $3$ .