Division of degrees with identical bases — lesson. Mathematics State Board, Class 7.

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When dividing degrees with the same base, the powers are subtracted, and the base remains unchanged.

a^{n} : a^{m} = a^{n - m}

Where

a \neq 0

, \(n\) and \(m\) are natural numbers such that n>m.

Important!

You cannot replace the value of the difference

a^{15} - a^{4}

a^{11}

The formula is applied from left to right, and from right to left.

Example:

Calculate:

5^{3} : 5

Answer:

5^{3} : 5 = 5^{3} : 5^{1} = 5^{3 - 1} = 5^{2} = 25

3^{7} : 3^{3}

Answer:

3^{7} : 3^{3} = 3^{7 - 3} = 3^{4} = 81

3. Simplify the expression.

\frac{t^{27}}{t^{14}}

Answer:

\frac{t^{27}}{t^{14}} = t^{27} : t^{14} = t^{27 - 14} = t^{13}

4. Make

2^{7}

as a ratio.

Answer: Exponent \(7\) can be represented as a difference in several ways:

\begin{array}{l} 2^{7} = 2^{9 - 2} = 2^{9} : 2^{2}; \\ 2^{7} = 2^{8 - 1} = 2^{8} : 2^{1} = 2^{8} : 2 . \end{array}

Did you find an error?

9. Division of degrees with identical bases