Answer
a) \( 3 x^{3} y^{4} z^{2} \times 8 x^{2} y^{4} z = 24 x^{5} y^{8} z^{3} \)
b) \( (9 x y z)^{6} = 9^{6} x^{6} y^{6} z^{6} \)
c) \( (9 x y z)^{1} = 9 x y z \)
d) \( -\left(3 a^{2} b\right)^{3} = -27 a^{6} b^{3} \)
e) \( x^{-5} \times x^{-3} = \frac{1}{x^{8}} \)
f) \( x^{-2} \times x^{6} = x^{4} \)
g) \( x^{3} \times x^{-7} = \frac{1}{x^{4}} \)
Solution
Simplify the expression by following steps:
- step0: Evaluate the power:
\(\left(9xyz\right)^{1}\)
- step1: Evaluate the power:
\(9xyz\)
Calculate or simplify the expression \( x^{3} \left(x^{-7}\right) \).
Simplify the expression by following steps:
- step0: Solution:
\(x^{3}\left(x^{-7}\right)\)
- step1: Evaluate:
\(x^{3}\times x^{-7}\)
- step2: Simplify the expression:
\(x^{3-7}\)
- step3: Subtract the numbers:
\(x^{-4}\)
- step4: Simplify:
\(\frac{1}{x^{4}}\)
Calculate or simplify the expression \( x^{-5} \cdot x^{-3} \).
Simplify the expression by following steps:
- step0: Solution:
\(x^{-5}\times x^{-3}\)
- step1: Simplify the expression:
\(x^{-5-3}\)
- step2: Subtract the numbers:
\(x^{-8}\)
- step3: Simplify:
\(\frac{1}{x^{8}}\)
Expand the expression \( 3 x^{3} y^{4} z^{2} \left(8 x^{2} y^{4} z\right) \)
Simplify the expression by following steps:
- step0: Simplify:
\(3x^{3}y^{4}z^{2}\left(8x^{2}y^{4}z\right)\)
- step1: Calculate:
\(3x^{3}y^{4}z^{2}\times 8x^{2}y^{4}z\)
- step2: Multiply the terms:
\(24x^{3}y^{4}z^{2}x^{2}y^{4}z\)
- step3: Multiply the terms:
\(24x^{3+2}y^{4}z^{2}y^{4}z\)
- step4: Add the numbers:
\(24x^{5}y^{4}z^{2}y^{4}z\)
- step5: Multiply the terms:
\(24x^{5}y^{4+4}z^{2}\times z\)
- step6: Add the numbers:
\(24x^{5}y^{8}z^{2}\times z\)
- step7: Multiply the terms:
\(24x^{5}y^{8}z^{2+1}\)
- step8: Add the numbers:
\(24x^{5}y^{8}z^{3}\)
Expand the expression \( (9 x y z)^{6} \)
Simplify the expression by following steps:
- step0: Use the properties of exponents:
\(\left(9xyz\right)^{6}\)
- step1: Use the properties of exponents:
\(9^{6}x^{6}y^{6}z^{6}\)
Expand the expression \( -\left(3 a^{2} b\right)^{3} \)
Simplify the expression by following steps:
- step0: Simplify:
\(-\left(3a^{2}b\right)^{3}\)
- step1: Simplify:
\(-27a^{6}b^{3}\)
Calculate or simplify the expression \( x^{-2} \left(x^{6}\right) \).
Simplify the expression by following steps:
- step0: Solution:
\(x^{-2}\left(x^{6}\right)\)
- step1: Evaluate:
\(x^{-2}\times x^{6}\)
- step2: Simplify the expression:
\(x^{-2+6}\)
- step3: Add the numbers:
\(x^{4}\)
Aquí están las soluciones a cada una de las expresiones:
a) \( 3 x^{3} y^{4} z^{2}\left(8 x^{2} y^{4} z\right) = 24 x^{5} y^{8} z^{3} \)
b) \( (9 x y z)^{6} = 9^{6} x^{6} y^{6} z^{6} \)
c) \( (9 x y z)^{1} = 9 x y z \)
d) \( -\left(3 a^{2} b\right)^{3} = -27 a^{6} b^{3} \)
e) \( x^{-5} \cdot x^{-3} = \frac{1}{x^{8}} \)
f) \( x^{-2} \left(x^{6}\right) = x^{4} \)
g) \( x^{3} \left(x^{-7}\right) = \frac{1}{x^{4}} \)
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