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$Express the following fraction in simplest form using only positive exponents. (6d^(4))/(2(d^(2))^(2)) Answer:$

Express the following fraction in simplest form using only positive exponents. $\newline$ $\frac{6 d^{4}}{2\left(d^{2}\right)^{2}}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

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

\newline

\frac{6 d^{4}}{2\left(d^{2}\right)^{2}}

\newline

Answer:

Write Expression and Identify Terms: Write down the given expression and identify the terms that can be simplified. $\newline$ The given expression is $(6d^{4})/(2(d^{2})^{2})$ . We need to simplify this expression by reducing the fraction and simplifying the exponents.
Simplify Denominator Exponent: Simplify the exponent in the denominator. $\newline$ The exponent in the denominator is $(d^{2})^{2}$ . According to the power of a power rule, $(a^{m})^{n} = a^{m*n}$ , we multiply the exponents. $\newline$ $(d^{2})^{2} = d^{2*2} = d^{4}$ .
Rewrite with Simplified Denominator: Rewrite the expression with the simplified denominator. $\newline$ Now the expression becomes $(6d^{4})/(2d^{4})$ .
Simplify Fraction by Canceling: Simplify the fraction by canceling out common terms. Both the numerator and the denominator have a common term $d^{4}$ , which can be canceled out. Also, the coefficient $6$ in the numerator can be divided by the coefficient $2$ in the denominator. $(\frac{6}{2})d^{4}/d^{4} = 3 \times (d^{4}/d^{4})$ .
Cancel out Common Terms: Cancel out the common $d^{4}$ terms. $\newline$ Since $\frac{d^{4}}{d^{4}}$ is equal to $1$ , we are left with $3 \times 1$ , which simplifies to $3$ .

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