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Simplify the following expressions: a) y9 ext div y4 b) racm7m5

Mathematics

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Answers

2 parts
a

y5y^5

b

m2m^2

Step-by-step solution

6 steps

Here are the solutions to the simplification problems.

Part a· 3 steps

Simplify y9÷y4y^9 \div y^4

  1. Apply the rule of exponents for division.

    When dividing terms with the same base, subtract the exponents: am÷an=am−na^m \div a^n = a^{m-n}.

  2. Substitute the given values into the rule.

    y9÷y4=y9−4y^9 \div y^4 = y^{9-4}
  3. Perform the subtraction in the exponent.

    y9−4=y5y^{9-4} = y^5

    The simplified expression is y5\boxed{y^5}.

Part b

m2m^2

Simplify m7m5\frac{m^7}{m^5}

  1. Apply the rule of exponents for division.

    When dividing terms with the same base, subtract the exponents: aman=am−n\frac{a^m}{a^n} = a^{m-n}.

  2. Substitute the given values into the rule.

    m7m5=m7−5\frac{m^7}{m^5} = m^{7-5}
  3. Perform the subtraction in the exponent.

    m7−5=m2m^{7-5} = m^2

    The simplified expression is m2\boxed{m^2}.

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