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$Express the following fraction in simplest form, only using positive exponents. (2h)/(-4(h^(-2))^(2)) Answer:$

Express the following fraction in simplest form, only using positive exponents. $\newline$ $\frac{2 h}{-4\left(h^{-2}\right)^{2}}$ $\newline$ Answer:

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Math Problems

Algebra 1

Multiplication with rational exponents

Full solution

Q. Express the following fraction in simplest form, only using positive exponents.

\newline

\frac{2 h}{-4\left(h^{-2}\right)^{2}}

\newline

Answer:

Identify Negative Exponent: Write down the given expression and identify the negative exponent. $\newline$ The given expression is $(2h)/(-4(h^{-2})^2)$ . $\newline$ We need to simplify this expression and express it with only positive exponents.
Simplify Denominator: Simplify the denominator by applying the power to the negative exponent. $\newline$ The denominator is $-4(h^{-2})^2$ . We need to square both the coefficient and the variable with the negative exponent. $\newline$ $(-4)^2 = 16$ $\newline$ $(h^{-2})^2 = h^{-4}$ $\newline$ So, the denominator becomes $16h^{-4}$ .
Rewrite Expression: Rewrite the expression with the simplified denominator. $\newline$ Now the expression is $(2h)/(16h^{-4})$ .
Remove Negative Exponent: Apply the property of exponents to remove the negative exponent by bringing it to the numerator. $\newline$ $h^{-4}$ in the denominator is the same as $h^4$ in the numerator. $\newline$ So, the expression becomes $(2h \cdot h^4)/16$ .
Combine Like Terms: Simplify the expression by combining like terms in the numerator. In the numerator, we have $2h \times h^4$ which simplifies to $2h^5$ . Now the expression is $\frac{2h^5}{16}$ .
Simplify Fraction: Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. $\newline$ The greatest common divisor of $2$ and $16$ is $2$ . $\newline$ Divide both the numerator and the denominator by $2$ . $\newline$ $\frac{2h^5}{2} / \frac{16}{2} = \frac{h^5}{8}$ .