Express the following fraction in simplest form using only positive exponents.start fraction, 4, p, to the power 4 , divided by, 3, left bracket, p, cubed, right bracket, cubed, end fraction3(p 3 ) 3 4p 4
Question
Express the following fraction in simplest form using only positive exponents.start fraction, 4, p, to the power 4 , divided by, 3, left bracket, p, cubed, right bracket, cubed, end fraction3(p 3 ) 3 4p 4
Solution
The given expression is 4p^4 / 3(p^3)^3.
Step 1: Simplify the denominator. The rule of exponents states that (a^m)^n = a^(mn). So, (p^3)^3 = p^(33) = p^9.
So, the expression becomes 4p^4 / 3p^9.
Step 2: Simplify the fraction. The rule of exponents states that a^m / a^n = a^(m-n). So, p^4 / p^9 = p^(4-9) = p^-5.
So, the expression becomes 4/3 * p^-5.
Step 3: Convert the negative exponent to a positive exponent. The rule of exponents states that a^-m = 1/a^m. So, p^-5 = 1/p^5.
So, the expression becomes 4/3 * 1/p^5 = 4/(3p^5).
So, the fraction 4p^4 / 3(p^3)^3 in simplest form using only positive exponents is 4/(3p^5).
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