**Multiplication with exponents :**

To simplify two or more exponent terms expressed in multiplication with same bases, we have to write the base once and add the powers.

Let us see some example problems based on the above concept.

**Example 1 :**

Find the value of the following

3⁻⁴ x 3⁻³

**Solution : **

Since we have same bases for both terms, we have to write the base once and add the powers.

3⁻⁴ x 3⁻³ = 3^(-4-3)

= 3^(-7)

In order to change the power as positive, we have to write the reciprocal form.

= 1/3⁷

**Example 2 :**

Find the value of the following

(2/8)^2 x ⋅ (2/8)^x = (2/8)^6

**Solution : **

Since we have same bases for both terms on the left side, we have to combine them

(2/8)^(2 x + x) = (2/8)^6

(2/8)^(3 x) = (2/8)^6

Since we have same bases on either sides of equal signs, we have to equate the powers

3x = 6

Divide 3 on both sides,

3x/3 = 6/3

x = 2

**Example 3 :**

Find the value of the following

(-2)⁻⁵ x (-2)^6

**Solution : **

Since we have same bases for both terms, we have to write the base once and add the powers.

(-2)⁻⁵ x (-2)^6 = (-2)^(- 5 + 6)

= (-2)^1

= -2

Hence the answer is -2.

**Example 4 :**

Find the value of the following

(-4)⁵ x (-4)⁸

**Solution : **

Since we have same bases for both terms, we have to write the base once and add the powers.

(-4)⁵ x (-4)⁸ = (-4)^(5 + 8)

= (-4)^13

Hence the answer is (-4)^13.

**Example 5 :**

Find the value of the following

(-3)⁴ ⋅ (5/3)⁴

**Solution : **

First we have to distribute the power 4 for both numerator and denominator.

(-3)⁴ ⋅ (5/3)⁴ = (-3)⁴ ⋅ (5⁴ / 3⁴)

Since we have even power, the base will become positive.

= (3)⁴ ⋅ (5⁴ / 3⁴)

= 5⁴

= 625

Hence the answer is 625.

**Example 6 :**

Find the value of the following

(4P)³⋅ (2P)² ⋅ P⁴

**Solution : **

First we have to distribute the powers 3 and 2.

(4P)³⋅ (2P)² ⋅ P⁴ = 4³ ⋅ p³ ⋅ 2² ⋅ P²⋅ P⁴

= 4³ ⋅ 2²⋅ p³⋅ P²⋅ P⁴

= 64 ⋅ 4 p^(3 + 2 + 4)

= 256 p^9

Hence the answer is 256 p^9.

After having gone through the stuff given above, we hope that the students would have understood "Multiplication with exponents".

Apart from the stuff given above, if you want to know more about "Multiplication with exponents", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**