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Simplify the following expressions: (30x)/(3x) and ((x3)/(22))^(-2).

Mathematics

ScanSolve AI Answer

Answer

10\text{10}

16x6\frac{16}{x^6}

Step-by-step solution

7 steps

  1. Simplify the numerical coefficients.

    303=10\frac{30}{3} = 10

  2. Simplify the variable terms.

    xx=x1−1=x0=1\frac{x}{x} = x^{1-1} = x^0 = 1

  3. Combine the simplified terms.

    10×1=1010 \times 1 = 10

    The simplified expression is:

    10\boxed{\text{10}}

  4. Simplify the denominator inside the parenthesis.

    22=42^2 = 4

    The expression becomes:

    (x34)−2\left(\frac{x^3}{4}\right)^{-2}

  5. Apply the negative exponent rule (a/b)−n=(b/a)n(a/b)^{-n} = (b/a)^n.

    (4x3)2\left(\frac{4}{x^3}\right)^2

  6. Apply the exponent to both the numerator and the denominator.

    42(x3)2\frac{4^2}{(x^3)^2}

  7. Evaluate the numerator and simplify the exponent in the denominator using (am)n=amn(a^m)^n = a^{mn}.

    16x3×2=16x6\frac{16}{x^{3 \times 2}} = \frac{16}{x^6}

    The simplified expression is:

    16x6\boxed{\frac{16}{x^6}}
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