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g100num [7]
3 years ago
14

What is the simplified expression for 7 power 4 multiplied by 7 power 6 over 7 power 8?

Mathematics
1 answer:
Masteriza [31]3 years ago
5 0

Answer:

The simplified expression of  \frac{7^{4}.7^{6}}{7^{8}} is 7² ⇒ C

Step-by-step explanation:

Let us revise some rules of exponent

  • a^{m} × a^{n} = a^{m+n}
  • \frac{a^{m}}{a^{n}} =  a^{m-n}

Let us solve the question

∵ The expression is \frac{7^{4}.7^{6}}{7^{8}}

→ By using the first rule above add the exponents of 7

∴  \frac{7^{4}.7^{6}}{7^{8}} = \frac{7^{4+6}}{7^{8}}

∴  \frac{7^{4}.7^{6}}{7^{8}} = \frac{7^{10}}{7^{8}}

→ By using the second rule above, subtract the exponents of 7

∵  \frac{7^{4}.7^{6}}{7^{8}} = 7^{10-8}

∴  \frac{7^{4}.7^{6}}{7^{8}} = 7²

∴ The simplified expression of  \frac{7^{4}.7^{6}}{7^{8}} is 7²

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Since the base is a regular quadrilateral, each of its 4 sides must have length
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The area of the base is then
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The volume of the prism is the product of its base area and height.
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The volume is 1575 cm³.
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