simplify (13^3)^4 using exponent rules. Write in exponential form
To simplify (13^3)^4 using exponent rules, we multiply the exponents.
The exponent outside the parentheses needs to be distributed to both the base and the exponent inside the parentheses.
(13^3)^4 can be written as 13^(3*4) since we multiply the exponents.
So the simplified exponential form is 13^12.
simplify each expression using exponent rules.
5^3×5^4
(5^3)^4
5^4/5^3
To simplify 5^3 × 5^4 using exponent rules, we can sum the exponents of the same base:
5^3 × 5^4 = 5^(3+4) = 5^7
To simplify (5^3)^4 using exponent rules, we can multiply the exponents:
(5^3)^4 = 5^(3*4) = 5^12
To simplify 5^4/5^3 using exponent rules, we can subtract the exponents of the same base:
5^4 / 5^3 = 5^(4-3) = 5^1 = 5
solve all these problems
a^0
-(a)^0
0^0
(-8)^0
-(-8)^0
a^0 = 1. Any number raised to the power of zero is equal to 1.
-(a)^0 = -1. The negative sign applies after raising the base to the power of zero, so it is equivalent to -(1).
0^0 is undefined. In mathematics, zero raised to the power of zero has no definite value and is therefore considered undefined.
(-8)^0 = 1. Similar to the first example, any number raised to the power of zero is equal to 1. The negative sign does not affect the result.
-(-8)^0 = -1. The negative sign applies after raising the base to the power of zero, so it is equivalent to -(1).
(x^?)^5=x^20
what's the missing exponent?
To find the missing exponent, we can use the property of exponentiation that states (a^b)^c = a^(b*c).
In this case, we have (x^?)^5 = x^20.
To make both sides of the equation match, we need the exponent of x on the left side, when raised to the power of 5, to equal 20.
This means that ? * 5 = 20.
If we divide both sides of the equation by 5, we get ? = 4.
Therefore, the missing exponent is 4.