Question

rules of exponents review
simplify the following expressions. use only positive exponents in your answer.
simplify \\((2x^3)(5x^5)\\)
simplify \\((7x^2)^5\\)
simplify \\(\frac{9x^6}{3x^4}\\)
simplify \\(6x^{-5}\\)

Explanation:

Step1: Multiply coefficients, add exponents

$(2x^3)(5x^5) = (2 \times 5)x^{3+5} = 10x^8$

Step2: Distribute exponent to factors

$(7x^2)^5 = 7^5 \times (x^2)^5 = 16807x^{10}$

Step3: Divide coefficients, subtract exponents

$\frac{9x^6}{3x^4} = \frac{9}{3}x^{6-4} = 3x^2$

Step4: Rewrite negative exponent as reciprocal

$6x^{-5} = \frac{6}{x^5}$

Answer:

1. $10x^8$
2. $16807x^{10}$
3. $3x^2$
4. $\frac{6}{x^5}$