simplify:
x^-7 x^4
5x^-4 x^4
7x^0 y^-3
1. x^-7*x^4 = X^-3 = 1/X^3.
2. 5x^-4*x^4 = 5x^0 = 5.
3. 7x^0*y^-3 = 7y^-3 = 7/Y^3.
NOTE: Remember to multiply the coefficients and add the exponents.
To simplify a product of variables with different exponents, you can use the rule of exponents that states:
x^a * x^b = x^(a + b)
Let's apply this rule to simplify the expressions you provided.
1. For x^-7 * x^4:
To simplify, add the exponents:
(-7 + 4) = -3
Therefore, x^-7 * x^4 can be written as x^-3.
2. For 5x^-4 * x^4:
Again, add the exponents:
(-4 + 4) = 0
Since any number raised to the power of 0 equals 1, we can simplify 5x^-4 * x^4 as 5.
3. For 7x^0 * y^-3:
Any number (except zero) raised to the power of 0 equals 1, so x^0 can be replaced with 1:
7 * 1 * y^-3 = 7 * y^-3.
Therefore, 7x^0 * y^-3 simplifies to 7y^-3.
To summarize:
x^-7 * x^4 simplifies to x^-3.
5x^-4 * x^4 simplifies to 5.
7x^0 * y^-3 simplifies to 7y^-3.