Simplify the following algebraic expressions: 1. (30x6)/(3x⁻²) 2. (x3/22)⁻²

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for the expressions:

1. Simplify the expression $\frac{30x^6}{3x^{-2}}$

Divide the numerical coefficients.
$\frac{30}{3} = 10$
Apply the exponent rule $\frac{a^m}{a^n} = a^{m-n}$ for the $x$ terms.
$x^6 \cdot x^{-(-2)} = x^{6 - (-2)} = x^{6+2} = x^8$
Combine the simplified numerical and variable parts.
$10x^8$
The simplified expression is:
$\boxed{10x^8}$
2. Simplify $\left(\frac{x^3}{2^2}\right)^{-2}$
Apply the exponent rule $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ and $(a^m)^n = a^{mn}$ .
$\frac{(x^3)^{-2}}{(2^2)^{-2}}$
Simplify the exponents in the numerator and denominator.
$\frac{x^{3 \times (-2)}}{2^{2 \times (-2)}} = \frac{x^{-6}}{2^{-4}}$
Apply the negative exponent rule $a^{-n} = \frac{1}{a^n}$ to move terms with negative exponents to the opposite part of the fraction.
$\frac{2^4}{x^6}$
Calculate the value of $2^4$ .
$2^4 = 2 \times 2 \times 2 \times 2 = 16$
Substitute the value back into the expression.
$\frac{16}{x^6}$
The simplified expression is:
$\boxed{\frac{16}{x^6}}$

Simplify the following algebraic expressions: 1. (30x6)/(3x⁻²) 2. ((x3)/(22))⁻²