Evaluate. (64^((7)/(10)))/(64^((1)/(5)))=

Recognize the problem: Recognize that the problem involves the division of two expressions with the same base raised to different exponents.Apply quotient rule for exponents: Apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponents: a^(m)/a^(n) = a^(m-n).Subtract the exponents: Subtract the exponents (7/10) - (1/5). Since 1/5 is equivalent to 2/10, the subtraction is (7/10) - (2/10).Perform the subtraction: Perform the subtraction: (7/10) - (2/10) = 5/10.Simplify the result: Simplify 5/10 to its lowest terms, which is 1/2.Apply the simplified exponent: Apply the simplified exponent to the base: 64^(1/2).Recognize the base: Recognize that 64^(1/2) is the square root of 64.Calculate the square root: Calculate the square root of 64, which is 8.

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Evaluate.

(64^((7)/(10)))/(64^((1)/(5)))=

Evaluate. $\newline$ $\frac{64^{\frac{7}{10}}}{64^{\frac{1}{5}}}=$

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Math Problems

Grade 6

Multiply two decimals: where does the decimal point go?

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Q. Evaluate.

\newline

\frac{64^{\frac{7}{10}}}{64^{\frac{1}{5}}}=

Recognize the problem: Recognize that the problem involves the division of two expressions with the same base raised to different exponents.
Apply quotient rule for exponents: Apply the quotient rule for exponents, which states that when dividing like bases, you subtract the exponents: $a^{m}/a^{n} = a^{(m-n)}$ .
Subtract the exponents: Subtract the exponents $(\frac{7}{10}) - (\frac{1}{5})$ . Since $\frac{1}{5}$ is equivalent to $\frac{2}{10}$ , the subtraction is $(\frac{7}{10}) - (\frac{2}{10})$ .
Perform the subtraction: Perform the subtraction: $(\frac{7}{10}) - (\frac{2}{10}) = \frac{5}{10}$ .
Simplify the result: Simplify $\frac{5}{10}$ to its lowest terms, which is $\frac{1}{2}$ .
Apply the simplified exponent: Apply the simplified exponent to the base: $64^{1/2}$ .
Recognize the base: Recognize that $64^{1/2}$ is the square root of $64$ .
Calculate the square root: Calculate the square root of $64$ , which is $8$ .