Examples with solutions for Multiplication of Powers: Number of terms

Exercise #1

828385= 8^2\cdot8^3\cdot8^5=

Video Solution

Step-by-Step Solution

All bases are equal and therefore the exponents can be added together.

828385=810 8^2\cdot8^3\cdot8^5=8^{10}

Answer

810 8^{10}

Exercise #2

2102726= 2^{10}\cdot2^7\cdot2^6=

Video Solution

Step-by-Step Solution

We use the power property to multiply terms with identical bases:

aman=am+n a^m\cdot a^n=a^{m+n} Keep in mind that this property is also valid for several terms in the multiplication and not just for two, for example for the multiplication of three terms with the same base we obtain:

amanak=am+nak=am+n+k a^m\cdot a^n\cdot a^k=a^{m+n}\cdot a^k=a^{m+n+k} When we use the mentioned power property twice, we could also perform the same calculation for four terms of the multiplication of five, etc.,

Let's return to the problem:

Keep in mind that all the terms in the multiplication have the same base, so we will use the previous property:

2102726=210+7+6=223 2^{10}\cdot2^7\cdot2^6=2^{10+7+6}=2^{23} Therefore, the correct answer is option c.

Answer

223 2^{23}

Exercise #3

Simplify the following equation:

45×4×42= 4^5\times4\times4^2=

Video Solution

Answer

45+1+2 4^{5+1+2}

Exercise #4

Simplify the following equation:

53×56×52= 5^3\times5^6\times5^2=

Video Solution

Answer

53+6+2 5^{3+6+2}

Exercise #5

Simplify the following equation:

97×93×95= 9^7\times9^3\times9^5=

Video Solution

Answer

97+3+5 9^{7+3+5}

Exercise #6

Simplify the following equation:

112×113×114= 11^2\times11^3\times11^4=

Video Solution

Answer

112+3+4 11^{2+3+4}

Exercise #7

Simplify the following equation:

21×22×23= 2^1\times2^2\times2^3=

Video Solution

Answer

21+2+3 2^{1+2+3}

Exercise #8

Simplify the following equation:

105×107×102= 10^5\times10^7\times10^2=

Video Solution

Answer

a'+b' are correct

Exercise #9

Simplify the following equation:

133×134×132= 13^3\times13^4\times13^2=

Video Solution

Answer

139 13^9

Exercise #10

Simplify the following equation:

154×15×153= 15^4\times15\times15^3=

Video Solution

Answer

158 15^8

Exercise #11

Simplify the following equation:

206×202×204= 20^6\times20^2\times20^4=

Video Solution

Answer

A'+C' are correct

Exercise #12

Simplify the following equation:

43×44×42= -4^3\times-4^4\times-4^2=

Video Solution

Answer

49 -4^9

Exercise #13

Simplify the following equation:

62×65×6= 6^2\times6^5\times6=

Video Solution

Answer

68 6^8

Exercise #14

Expand the following expression:

76= 7^6=

Video Solution

Answer

71×7×74 7^1\times7\times7^4

Exercise #15

Expand the following equation:

810= 8^{10}=

Video Solution

Answer

83×83×84 8^3\times8^3\times8^4

Exercise #16

Expand the following equation:

612= 6^{12}=

Video Solution

Answer

62×63×67 6^2\times6^3\times6^7

Exercise #17

Expand the following equation:

54= 5^4=

Video Solution

Answer

5×5×52 5\times5\times5^2

Exercise #18

Reduce the following equation:

23×24×26×25= 2^3\times2^4\times2^6\times2^5=

Video Solution

Answer

218 2^{18}

Exercise #19

Reduce the following equation:

63×65×66×64= 6^3\times6^5\times6^6\times6^4=

Video Solution

Answer

618 6^{18}

Exercise #20

((x14×32×63)14)8= ((x^{\frac{1}{4}}\times3^2\times6^3)^{\frac{1}{4}})^8=

Video Solution

Answer

x12×34×66 x^{\frac{1}{2}}\times3^4\times6^6