List any two uses of eponents in letters
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One of the trickiest concepts in algebra involves the manipulation of exponents, or powers. Many times, problems will require you to use the laws of exponents to simplify variables with exponents, or you will have to simplify an equation with exponents to solve it. To work with exponents, you need to know the basic exponent rules.
Structure of an Exponent
Exponent examples look like 2³, which would be read as two to the third power or two cubed, or 7^6, which would be read as seven to the sixth power. In these examples, 2 and 7 are the coefficient or base values while 3 and 6 are the exponents or powers. Exponent examples with variables look like x⁴ or 9y², where 1 and 9 are the coefficients, x and y are the variables and 4 and 2 are the exponents or powers.
1)Negative Exponents
To eliminate negative exponents, put the term under 1 and change the exponent so that the exponent is positive. For example, x^-6 is the same number as 1/(x^6). Flip fractions with negative exponents in order to make the exponent positive: (2/3)·³ equals (3/2)³. When division is involved, move variables from the bottom to the top or vice versa to make their exponents positive. For example, 8·²÷2·⁴=(1/8)²÷(1/2)⁴=(1/64)÷(1/16)=(1/64)x(16)=4.
2)Power of a Power
When a term that includes variables with exponents is raised to another power, raise the coefficient to that power and multiply each existing power by the second power to find the new exponent. For instance, (5x^6y²)² would simplify to 25x¹²y⁴.