Question

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LAWS OF EXPONENTS​

Answer 1

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The "Laws of Exponents" (also called "Rules of Exponents") come from three ideas: The exponent says how many times to use the number in a multiplication. A fractional exponentlike 1/n means to take the nth root: If you understand those, then you understand exponents!

We know how to calculate the expression 5 x 5.
This expression can be written in a shorter way using something called exponents.

5 × 5

= 5²

An expression that represents repeated multiplication of the same factor is called a power.

The number 5 is called the base, and the number 2 is called the exponent.
The exponent corresponds to the number of times the base is used as a factor.

Here are some examples :-

3¹

3 to the first power3

4²

4 to the second power or 4 squared

4 × 4

5³

5 to the third power or 5 cubed

5 × 5 × 5

2^6

2 to the power of six

=2 × 2 × 2 × 2 × 2 × 2

$\huge{Multiplication}$

If two powers have the same base then we can multiply the powers. When we multiply two powers we add their exponents.

The rule:

x^a × x^b

= x^a+b

Examples :

4² + 4²

= 4²+²

= 4 ⁴

$\huge{Divion}$

If two powers have the same base then we can divide the powers. When we divide powers we subtract their exponents.

The rule :

x⁴/x²

= x⁴-²

= x²

Example :

5⁴/5²

= 5⁴-²

= 5²

A negative exponent is the same as the reciprocal of the positive exponent.

x^-a

= 1/x^a

Example :

(4)-²

= 1/4²

When you raise a product to a power you raise each factor with a power.

(x × y)^a

Example :

(2x)⁴

= 2⁴ × 6⁴

= 16x⁴

The rule for the power of a power and the power of a product can be combined into the following rule :

( x^a × y^b )^z = x^a×z × y^b×z

Example :

(x² × y²)³

= x²×³ × x²×³

x^6 × x^6

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$\huge{Thankyou}$

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Answer 2

Answer:

$hey dear here's your answer$

Laws of Exponents Laws of Exponents. When multiplying like bases, keep the base the same and add the exponents. When raising a base with a power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

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